Use Power Series Operations to Find the Taylor Series at X

question 91

Multiple Choice

Use power series operations to find the Taylor series at x = 0 for the given function.
- $$x ^ { 8 } e ^ { x }$$

• A) \(\sum _ { n = 0 } ^ { \infty } \frac { 8 ^ { n _ { x ^ { n } } } } { n ! }\)
• B) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { n + 8 } } { n ! }\)
• C) \(\sum _ { n = 0 } ^ { \infty } \frac { 8 ^ { n _ { x } n } } { ( n + 8 ) ! }\)
• D) \(\sum _ { n = 0 } ^ { \infty } \frac { x ^ { n + 8 } } { ( n + 8 ) ! }\)

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Definitions:

Ø30 f7 Fit

A specification for a cylindrical fit where Ø30 defines the nominal diameter in millimeters and f7 specifies the tolerance class for a hole.

High Precision Fit

Refers to a high degree of accuracy in the mating of two machine parts, ensuring minimal play or clearance between them.

H8/f7 Fit

A specific tolerance class designation for holes (H8) and shafts (f7) in engineering, ensuring a precise interference fit.

Basis

The underlying support or foundation for an idea, argument, or process; in materials, it could refer to the primary component or substance that forms the starting point.